how much is a one day ticket to the forbidden city?

CNY 40 during Nov. 1 and the next Mar. 31;
CNY 60 during Apr. 1 and Oct. 31;
CNY 10 for the Treasure Gallery;
CNY 10 for the Clock and Watch Gallery.

i'm sorry to sound uncultured, but a) what is cny and b) the dates don't make any sense; does that mean it's that price for the duration of november-march or what?

CNY would be like saying USD. It's ChiNese Yuan. And yes, nearly everything in China-especially in BJ has two listed prices. It'll have a listed price for the "peak season" or the "busy season" which is when all of the tourists are here. Those prices are going to be higher, like here it's listed for 60CNY. That season is from April until October. After that, from November to the next March is the low season, and the prices will be a lot lower during that time.